'The modern view that emerged from Maxwell's theory is a world with two layers. The first layer, the layer of fundamental constituents, consists of fields satisfying simple linear equations. The second layer, the layer of things that we can directly touch and measure, consists of mechanical stresses, energies and forces. The two layers are connected, because the quantities on the second layer are quadratic or bilinear combinations of the quantities on the first layer. To calculate the energies or the stresses, you take the square of the electric field strength or multiply one component of the field by another. The two-layer structure of the world is the basic reason why Maxwell's theory seems so mysterious and difficult. The objects of the first layer are abstractions not directly accessible to our senses. The objects that we can feel and touch are on the second layer, and their behaviour is only determined indirectly by the equations that operate on the first layer. The two layer structure implies that the basic processes of nature are hidden from our view'.

Antenna measurement data is collected over a tabulating surface as a function of position relative to the antenna under test (AUT). In the far -field, where most antenna pattern comparisons are performed, this reduces to the problem of representing data as a function of one or more angles with the electrically large measurement radius being arbitrary but fixed. In general, even when taking conventional far -field data, the antenna measurement engineer seldom uses a single rotation stage as two-dimensional pattern data is generally required. However, as will be illustrated below, the data collection/visualisation coordinate system directly affects how data is mapped to the surface: planar, cylindrical, spherical or other types. Thus, far -field measurements are usually mapped or converted to spherical surfaces from which directivity, polarisation and patterns are calculated and projected. Often the collected coordinate system is not the same as the fmalmapped system, requiring special formulas for proper conversion. In addition, projecting this data in two- and three-dimensional polar or rectangular plots presents other problems in interpreting the antenna pattern data. Implicit within this is the assumption that the tabulating grids are plaid, monotonic and equally spaced. Whilst not necessary from a theoretical standpoint, these conditions greatly simplify the recording process for a robotic positioner as well as simplifying the tasks of numerical integration, differentiation and interpolation. The following sections present a concise description of the most important coordinate systems and then go on to discuss methods for representing the relationships between them. This section presents a summary of many of the most commonly encountered coordinate system formulas and shows how they relate to one another.

This chapter has described the basic geometry and operation of a conventional planar near-field scanner. It has done this by examining the separate sub-systems employed in a scanner facility - primarily the RF sub-system, the robotic positioned sub-system and the range antennas or probes that would be used in the measurement process.